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Table 1 Statistical power of the UEMS total sum score model M1 for all simulation settings (1:1 allocation) compared with that of conventional approaches

From: Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes

Experimental conditions (1:1 allocation) Novel model-based methods Conventional approaches
N total N trtmt N ctrl Odds ratio Asymptotic ePolr test based on model M1 Permutated ePolr test based on model M1 t-test M1 Wilcoxon rank sum test M1 ANCOVA M1
80 40 40 1.00 .062 [.058,.067] .049 [.045,.052] .049 [.046,.053] .049 [.045,.052] .048 [.045,.052]
120 60 60 1.00 .061 [.057,.065] .050 [.046,.053] .053 [.049,.056] .050 [.046,.053] .052 [.049,.056]
160 80 80 1.00 .058 [.054,.062] .046 [.042,.049] .049 [.046,.053] .048 [.045,.051] .049 [.045,.052]
200 100 100 1.00 .057 [.054,.061] .048 [.045,.052] .048 [.044,.051] .047 [.044,.051] .048 [.045,.052]
240 120 120 1.00 .061 [.058,.065] .053 [.049,.056] .053 [.049,.056] .052 [.048,.055] .052 [.049,.056]
80 40 40 1.25 .105 [.099,.111] .086 [.082,.091] .077 [.073,.082] .074 [.070,.078] .079 [.074,.083]
120 60 60 1.25 .124 [.119,.130] .103 [.098,.108] .091 [.086,.095] .089 [.084,.093] .091 [.086,.095]
160 80 80 1.25 .142 [.137,.148] .122 [.117,.128] .103 [.098,.108] .104 [.099,.109] .106 [.101,.111]
200 100 100 1.25 .162 [.156,.168] .142 [.136,.148] .124 [.119,.129] .122 [.117,.128] .127 [.122,.132]
240 120 120 1.25 .182 [.176,.189] .162 [.156,.168] .136 [.131,.142] .135 [.130,.141] .139 [.133,.145]
80 40 40 1.50 .194 [.186,.202] .164 [.158,.170] .145 [.139,.151] .143 [.137,.148] .146 [.140,.151]
120 60 60 1.50 .265 [.258,.273] .233 [.227,.240] .194 [.188,.200] .195 [.189,.202] .199 [.193,.205]
160 80 80 1.50 .328 [.321,.336] .298 [.290,.305] .243 [.236,.250] .241 [.234,.248] .246 [.239,.253]
200 100 100 1.50 .393 [.385,.401] .364 [.356,.371] .289 [.281,.296] .290 [.282,.297] .296 [.288,.303]
240 120 120 1.50 .447 [.439,.455] .416 [.408,.424] .331 [.324,.339] .334 [.327,.342] .339 [.332,.347]
80 40 40 1.75 .294 [.285,.303] .260 [.253,.268] .225 [.218,.232] .221 [.214,.228] .227 [.221,.234]
120 60 60 1.75 .424 [.415,.432] .384 [.376,.392] .325 [.318,.333] .321 [.314,.329] .327 [.320,.335]
160 80 80 1.75 .533 [.525,.541] .497 [.489,.505] .408 [.400,.416] .407 [.399,.415] .414 [.406,.422]
200 100 100 1.75 .630 [.622,.638] .596 [.589,.604] .492 [.484,.500] .494 [.486,.502] .499 [.491,.507]
240 120 120 1.75 .709 [.701,.716] .678 [.670,.685] .569 [.561,.577] .575 [.567,.583] .576 [.568,.584]
80 40 40 2.00 .430 [.420,.440] .383 [.375,.391] .320 [.312,.327] .315 [.308,.323] .323 [.315,.330]
120 60 60 2.00 .586 [.578,.595] .543 [.535,.551] .458 [.450,.466] .460 [.452,.468] .462 [.454,.470]
160 80 80 2.00 .719 [.712,.727] .685 [.677,.692] .574 [.566,.582] .579 [.571,.587] .580 [.572,.588]
200 100 100 2.00 .805 [.799,.812] .782 [.776,.789] .676 [.668,.683] .681 [.673,.688] .681 [.673,.688]
240 120 120 2.00 .862 [.856,.867] .846 [.840,.852] .750 [.743,.757] .753 [.746,.760] .756 [.749,.763]
80 40 40 2.25 .534 [.524,.543] .488 [.480,.496] .428 [.420,.436] .421 [.413,.429] .426 [.418,.434]
120 60 60 2.25 .717 [.709,.724] .678 [.671,.686] .588 [.581,.596] .591 [.583,.599] .591 [.583,.599]
160 80 80 2.25 .832 [.826,.838] .809 [.803,.815] .707 [.700,.715] .710 [.703,.717] .712 [.704,.719]
200 100 100 2.25 .905 [.900,.909] .887 [.882,.892] .797 [.791,.804] .801 [.795,.808] .802 [.795,.808]
240 120 120 2.25 .950 [.946,.953] .941 [.937,.945] .873 [.868,.879] .876 [.871,.881] .877 [.871,.882]
80 40 40 2.50 .637 [.627,.646] .588 [.580,.595] .509 [.501,.517] .504 [.496,.512] .508 [.500,.516]
120 60 60 2.50 .816 [.809,.822] .783 [.776,.789] .689 [.682,.697] .694 [.686,.701] .693 [.685,.700]
160 80 80 2.50 .909 [.904,.913] .892 [.887,.897] .807 [.801,.814] .808 [.802,.815] .813 [.807,.819]
200 100 100 2.50 .957 [.954,.960] .948 [.944,.951] .888 [.882,.893] .889 [.883,.894] .891 [.885,.895]
240 120 120 2.50 .983 [.981,.985] .979 [.977,.982] .934 [.930,.938] .936 [.932,.940] .936 [.932,.940]
80 40 40 2.75 .715 [.706,.724] .677 [.669,.684] .597 [.590,.605] .591 [.583,.599] .599 [.591,.607]
120 60 60 2.75 .881 [.875,.886] .856 [.850,.862] .775 [.768,.782] .776 [.769,.783] .777 [.771,.784]
160 80 80 2.75 .952 [.948,.955] .941 [.937,.945] .884 [.879,.889] .886 [.881,.891] .888 [.882,.893]
200 100 100 2.75 .981 [.979,.983] .977 [.975,.979] .937 [.933,.941] .940 [.936,.944] .940 [.936,.944]
240 120 120 2.75 .994 [.992,.995] .992 [.990,.993] .972 [.969,.975] .973 [.970,.975] .974 [.972,.977]
80 40 40 3.00 .781 [.773,.789] .743 [.736,.750] .665 [.657,.672] .660 [.653,.668] .665 [.657,.673]
120 60 60 3.00 .926 [.922,.930] .908 [.903,.913] .841 [.835,.847] .841 [.835,.847] .843 [.837,.849]
160 80 80 3.00 .975 [.973,.978] .968 [.965,.971] .929 [.925,.933] .929 [.925,.933] .930 [.926,.934]
200 100 100 3.00 .992 [.991,.994] .990 [.988,.992] .967 [.964,.969] .968 [.965,.970] .969 [.966,.972]
240 120 120 3.00 .998 [.997,.999] .997 [.997,.998] .987 [.985,.989] .988 [.986,.989] .988 [.986,.989]
  1. Point estimates of the statistical power and 95% Wilson confidence intervals are reported